Towards Privacy Protection in Smart Grid

The smart grid is an electronically controlled electrical grid that connects power generation, transmission, distribution, and consumers using information communication technologies. One of the key characteristics of the smart grid is its support for bi-directional information flow between the consumer of electricity and the utility provider. This two-way interaction allows electricity to be generated in real-time based on consumers’ demands and power requests. As a result, consumer privacy becomes an important concern when collecting energy usage data with the deployment and adoption of smart grid technologies. To protect such sensitive information it is imperative that privacy protection mechanisms be used to protect the privacy of smart grid users. We present an analysis of recently proposed smart grid privacy solutions and identify their strengths and weaknesses in terms of their implementation complexity, efficiency, robustness, and simplicity.     

Optimum synthesis of discrete capacitated networks with multi-terminal commodity flow requirements

Network design problems arise in a wide range of applied areas including telecommunications, computer networks, and transportation. In this paper, we address the following discrete capacitated multi-terminal network design problem. Given a connected digraph G = (V,A), a set of L potential facilities to be installed on each arc, and a set of K multi-terminal (non-simultaneous) commodity flow requirements, the problem is to find a set of facilities to install in order to route the K nonsimultaneous flows while minimizing the total fixed plus variable costs. We describe an exact procedure for solving this problem based on Benders decomposition. Our algorithm includes several features that significantly improve the efficiency of the basic approach. Computational results attest to the efficacy of the proposed algorithm, which can solve medium- to large-scale problems to optimality.     

Enhancing RLT relaxations via a new class of semidefinite cuts

In this paper, we propose a mechanism to tighten Reformulation-Linearization Technique (RLT) based relaxations for solving nonconvex programming problems by importing concepts from semidefinite programming (SDP), leading to a new class of semidefinite cutting planes. Given an RLT relaxation, the usual nonnegativity restrictions on the matrix of RLT product variables is replaced by a suitable positive semidefinite constraint. Instead of relying on specific SDP solvers, the positive semidefinite stipulation is re-written to develop a semi-infinite linear programming representation of the problem, and an approach is developed that can be implemented using traditional optimization software. Specifically, the infinite set of constraints is relaxed, and members of this set are generated as needed via a separation routine in polynomial time. In essence, this process yields an RLT relaxation that is augmented with valid inequalities, which are themselves classes of RLT constraints that we call semidefinite cuts. These semidefinite cuts comprise a relaxation of the underlying semidefinite constraint. We illustrate this strategy by applying it to the case of optimizing a nonconvex quadratic objective function over a simplex. The algorithm has been implemented in C++, using CPLEX callable routines, and two types of semidefinite restrictions are explored along with several implementation strategies. Several of the most promising lower bounding strategies have been implemented within a branch-and-bound framework. Computational results indicate that the cutting plane algorithm provides a significant tightening of the lower bound obtained by using RLT alone. Moreover, when used within a branch-and-bound framework, the proposed lower bound significantly reduces the effort required to obtain globally optimal solutions.     

Two-stage stochastic hierarchical multiple risk problems: models and algorithms

In this paper, we consider a class of two-stage stochastic risk management problems, which may be stated as follows. A decision-maker determines a set of binary first-stage decisions, after which a random event from a finite set of possible outcomes is realized. Depending on the realization of this outcome, a set of continuous second-stage decisions must then be made that attempt to minimize some risk function. We consider a hierarchy of multiple risk levels along with associated penalties for each possible scenario. The overall objective function thus depends on the cost of the first-stage decisions, plus the expected second-stage risk penalties. We develop a mixed-integer 0–1 programming model and adopt an automatic convexification procedure using the reformulation–linearization technique to recast the problem into a form that is amenable to applying Benders’ partitioning approach. As a principal computational expedient, we show how the reformulated higher-dimensional Benders’ subproblems can be efficiently solved via certain reduced-sized linear programs in the original variable space. In addition, we explore several key ingredients in our proposed procedure to enhance the tightness of the prescribed Benders’ cuts and the efficiency with which they are generated. Finally, we demonstrate the computational efficacy of our approaches on a set of realistic test problems. Dr. H. D. Sherali acknowledges the support of the National Science Foundation under Grant No. DMI-0552676. Dr. J. C. Smith acknowledges the support of the Air Force Office of Scientific Research under Grant No. AFOSR/MURI F49620-03-1-0477.     

Solutions and optimality criteria for nonconvex constrained global optimization problems with connections between canonical and Lagrangian duality

This paper presents a canonical duality theory for solving a general nonconvex quadratic minimization problem with nonconvex constraints. By using the canonical dual transformation developed by the first author, the nonconvex primal problem can be converted into a canonical dual problem with zero duality gap. A general analytical solution form is obtained. Both global and local extrema of the nonconvex problem can be identified by the triality theory associated with the canonical duality theory. Illustrative applications to quadratic minimization with multiple quadratic constraints, box/integer constraints, and general nonconvex polynomial constraints are discussed, along with insightful connections to classical Lagrangian duality. Criteria for the existence and uniqueness of optimal solutions are presented. Several numerical examples are provided.     

Two-stage workforce planning under demand fluctuations and uncertainty

We address a multi-category workforce planning problem for functional areas located at different service centres, each having office-space and recruitment capacity constraints, and facing fluctuating and uncertain workforce demand. A deterministic model is initially developed to deal with workforce fluctuations based on an expected demand profile over the horizon. To hedge against the demand uncertainty, we also propose a two-stage stochastic program, in which the first stage makes personnel recruiting and allocation decisions, while the second stage reassigns workforce demand among all units. A Benders’ decomposition-based algorithm is designed to solve this two-stage stochastic mixed-integer program. Computational results based on some practical numerical experiments are presented to provide insights on applying the deterministic versus the stochastic programming approach, and to demonstrate the efficacy of the proposed algorithm as compared with directly solving the model using its deterministic equivalent.     

Vehicular ad hoc networks (VANETS): status, results, and?challenges

Recent advances in hardware, software, and communication technologies are enabling the design and implementation of a whole range of different types of networks that are being deployed in various environments. One such network that has received a lot of interest in the last couple of years is the Vehicular Ad-Hoc Network (VANET). VANET has become an active area of research, standardization, and development because it has tremendous potential to improve vehicle and road safety, traffic efficiency, and convenience as well as comfort to both drivers and passengers. Recent research efforts have placed a strong emphasis on novel VANET design architectures and implementations. A?lot of VANET research work have focused on specific areas including routing, broadcasting, Quality of Service (QoS), and security. We survey some of the recent research results in these areas. We present a review of wireless access standards for VANETs, and describe some of the recent VANET trials and deployments in the US, Japan, and the European Union. In addition, we also briefly present some of the simulators currently available to VANET researchers for VANET simulations and we assess their benefits and limitations. Finally, we outline some of the VANET research challenges that still need to be addressed to enable the ubiquitous deployment and widespead adoption of scalable, reliable, robust, and secure VANET architectures, protocols, technologies, and services.